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KEY POINTS

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Published in: Geography
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Surface Area & Volumes, Class IX, CBSE Board

Arun M / Faridabad

4 years of teaching experience

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Teaches: Mathematics, IIT JEE Mains

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  1. February 26 Surface 2016 Areas & Volume ( CLASS , CBSE BOARD ) KEY POINTS
  2. CUBOID : A solid bounded by SIX rectangular plane surfaces ( faces ) is called a CUBOID. There are twelve edges and eight vertices of a cuboid. Opposite faces are parallel and equal. Cuboid is as shown below -- Cuboid Let length of cuboid is l, breadth is b and height is h respectively. Then Total surface area of cuboid = 2 ( 1b + bh + lh ) sq. units. • Lateral surface area of cuboid = 2 ( I + b ) h sq. units (Excluding Top and Bottom faces • Length of Diagonal of a cuboid = (12 + b2 + h ) units. 2 1/2 Volume of cuboid = I x b x h cubic units CUBE : A solid bounded by SIX CONGURENT SQUARE surfaces ( faces ) is called a CUBE. There are twelve edges and eight vertices of a cube. Opposite faces are parallel and congruent. Cube is as shown below - Cube Let its length, breadth and height are all equal to a i.e. all edges are equal to a. Then Total surface area of cube = 6 a2 sq. units. • Lateral surface area of cube = 4 a2 sq. units (Excluding Top and Bottom faces — a (3)1/2 units. • Length of Diagonal of a cube
  3. Volume of cube — a cubic units RIGHT CIRCULAR CYLINDER : A solid generated by the revolution of a rectangle about one of its sides is called a cylinder. It has one curved face and two circular faces. Cylinder is as shown below - Cylinder Let radius of Solid cylinder is r and its height is h respectively. Then Lateral ( Curved ) surface area of cylinder = 27trh sq. units. • Top surface Area = Bottom surface Area = 7tr2 sq. units. • Total surface area of cylinder = 27trh + 27tr2 27tr ( h + r) sq. units Volume of cylinder = 7tr2h cubic units Let External radius of Hollow cylinder is R, Internal radius r and its height is h respectively. Then Outer Lateral surface area of cylinder 27tRh sq. units. Internal Lateral surface area of cylinder 27trh sq. units. Total Lateral surface area of cylinder = 27tRh + 27trh = 27th ( R + r) sq. units Top surface Area = Bottom surface Area = TtR2 - ar 2 — Tt(R2 r2) Total surface area of hollow cylinder = 27th (R + r) + 7t(R2 12 ) sq. units Material volume of hollow cylinder = 7tR2h - 7tr2h = 7th (R2 - r2 cubic units RIGHT CIRCULAR CONE : A solid generated by the revolution of a RIGHT triangle about one of its sides containing the right angle is called right circular cone. It has one curved face and one circular base. Cone is as shown below -
  4. Cone Let radius of cone is r, its height is h and slant height is I respectively. Then ( h2 + r2) 1/2 units. Slant height Lateral ( Curved ) surface area of cone = 7trl sq. units Bottom surface Area = 7tr2 sq. units. Total surface area of cylinder = 7trl + 7tr2 = ar ( I + r) sq. units Volume of cylinder = 1/3 x 7tr h cubic units SPHERE : A Sphere is a collection of points, in space, equidistant from a fixed point. The fixed point is called the centre and the fixed distance, the radius of the sphere. It has only one curved face. Sphere is as shown below - Sphere Let radius of Solid sphere is r. Then 47tr2 sq. units. Surface area of sphere • Volume of sphere = 4/3 x 7tr3 cubic units
  5. Let External radius of Hollow sphere ( SHELL )is R and Internal radius r respectively. Then 47tR2 sq. units. Outer surface surface area of shell = 47tr2 sq. units. Internal surface area of shell Total surface area of shell = 47tR2 + 47tr2 = 47t ( R2 + 12 ) sq. units Material volume of the shell = 4/3 x 7tR3 - 4/3 x Ttr3 = 4/3 x ( R3 - r3) cubic units HEMISPHERE : If a sphere is cut into two equal parts we get a hemisphere ( Half Sphere ). It has one curved face and one circular face. Let radius of hemisphere is r. Then = 27tr2 sq. units. • Curved surface area of hemisphere Surface area of circular face = ar sq. units. Total surface area of hemisphere = 27tr + 7tr2= 37tr2 sq. units = 2/3 x 7tr3 cubic units • Volume of hemi sphere Let External radius of Hemispherical SHELL is R and Internal radius is r respectively. Then = 27tR2 sq. units. Outer surface surface area of shell Internal surface area of shell = 27tr2 sq. units. Surface area of circular ring = 7tR2 - 7tr2 Total surface area of shell = 27tR2 + 27tr2 + (TtR2 - 7tr2 )= 7t ( 3R2 - 12 ) sq. units Material volume of the shell = 2/3 x 7tR3 - 2/3 x Ttr3 = 2/3 x It (R3 - r3) cubic units Please Note : If thickness of Hollow sphere ( SHELL ) or Hemispherical SHELL is t, t = (D—d )/2 units then t = R-r units OR where D and d are external and internal diameters of Hollow sphere ( SHELL ) or Hemispherical SHELL respectively.

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